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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -3, 'A8': -1, 'A9': 0, 'Lhash': '374231784193537715', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1335.9770762180428, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [11, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '167310.1', 'coefficient_field': '1.1.1.1', 'conductor': 167310, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1, 3, 7], [1, 1], [1], [1, 2, 17], [1, 2, 19], [1, 3, 23], [1, 1, 29], [1, 7, 31], [1, -2, 37], [1, -5, 41], [1, -11, 43], [1, -11, 47], [1, 11, 53], [1, 6, 59], [1, 14, 61], [1, 14, 67], [1, -6, 71], [1, 11, 73], [1, 8, 79], [1, -8, 83], [1, 6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 133, 'label': '2-167310-1.1-c1-0-133', 'leading_term': '7.91762315583', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'origin': 'EllipticCurve/Q/167310/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.4565857255114594, -1.38212600281112, -1.663712283528771, -0.445123770970552, 1.624115128018409, 2.499140474333909, 0.9264094634849745, -1.591828971253779, -2.153404990940651, -0.2252887044387675, 1.283120192093185, 0.02357712389283513, -1.970217239564164, -0.9805945770322387, 2.326643973534898, 3.193715124912119, 0.3486501958945533, -0.8461495351236159, 3.759745779022624, 9.637656485808433, 9.335299802930018, 3.571227731188162, -0.08376619581836627, 1.001258437229026, 1.69132641205684, -0.8489688099454228, -2.499967557265197, -0.5812661109899554, 1.135870181139519, 0.02656838844677825, -0.4727942692964072, 1.69146580960583, 2.539662303501392, -0.1115263109438999, -2.053325087752815, -0.8056912280906554, 0.05545910903898324, -0.9571917957626342, -0.119452760008496, 2.772132082101495, 2.889706316770619, 0.2224990314875161, -0.417380410534795, -0.002122114609532957, -3.104561169351103, -6.491996323866342, -4.149058936610288, 0.006712595200249519, -0.5796553646033125, -1.976255105563688, 0.79115315421783, 2.009101852898326, -1.713228572441828, -1.623145842215725, 5.362708204502086, 7.793788897953174, 1.547300838918762, -1.52522180423848, 3.101065623916453, 5.033300863274347, 0.8820553338534167, -1.121333605259004, 0.3380971703891617, -0.2084601414806662, -1.067979459336366, 0.7909993327035612, 0.8482706443198447, -1.937984725745455, -1.402556243526711, 1.497708287746881, 0.1980617315240466, -2.473553531362732, -0.7471223620500048, 1.25835283569127, -0.1727091825976991, -0.4232369195009259, 1.163979291411204, 0.2389786152296364, -0.7819526481749938, 0.8752709497051941, 0.3373146582228209, -1.816467841727187, 1.305252484323585, 4.760736420407945, 0.04031514368186177, -4.483003342115998, -0.426424189295144, 2.234583592914434, -1.799385153678404, -2.122531666149069, 1.317247055817108, -1.670034913545465, -5.92018997006826, -2.489517915800183, 0.5661994423696933, -1.75538067531465, -0.2479336061159946, 4.228701225381019, 1.765891361521718, -2.744753713853208, -0.9127084747344931, 1.2187475825165, -0.2468624787053511, 0.1303460390299963, 0.962669561900962, -1.145841749451405, -1.074801749205306, 1.260293812267602, -0.278995652311252, -2.212430923593842, -0.2831643552178485, -0.4038457123737619, -2.836428482846273, -1.234172042659609, 0.8244905671384926, -0.3942110158664579, 0.6582046893808943, 2.146904034158781, -1.297701991940876, -2.017984478001836], 'positive_zeros': ['1.055428487996775', '1.837313146999062', '2.524282832153559', '3.002536844199132', '3.577992414965081', '4.278227978179496', '4.577993330050674', '5.730751387772781', '5.856076737652396', '6.431765845667323', '7.055173964251109', '7.504100941044247', '7.825804683934222', '8.491408930186791', '9.145833470561316', '9.274872848738009', '9.761651607486417', '10.52634971297561', '10.86766959253837', '10.99946393765791', '11.99921716497429', '12.18349487811553', '12.69527044786663', '13.14785459627139', '13.57116539007856', '14.31126746906524', '14.60853249272893', '15.30474821645831', '15.68727373416145', '15.96770289506091', '16.41053948924557', '16.83026058533597', '17.35662670728747', '17.76450509277425', '18.31019800036214', '18.72659814039390', '19.06366149002078', '19.53023739063785', '19.88445720256168'], 'prelabel': '2-167310-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.551020180263684, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 374231784193537715, 'z1': {'__RealLiteral__': 0, 'data': '1.055428487996775', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.837313146999062', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.524282832153559', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1335.9770762180428, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 167310, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, -3, -1, 0, 1, -1, 0, 0, 3, 0, 1, -2, 0, -2, -1, 0, 1, -3, 0, 1, 0, 0, -3, -1, 0, -7, -1, 0, 2, 3, 0, 2, 2, 0, 1, 5, 0, 11, -1, 0, 3, 11, 0, 2, -1, 0, 0, -11, 0, 1, 3, 0, 1, -6, 0, -14, 7, 0, 1, 0, 0, -14, -2, 0, -3, 6, 0, -11, -2, 0, -2, 3, 0, -8, -1, 0, -5, 8, 0, 2, -11, 0, 1, -6, 0, 0, -3, 0, -11, 2, 0, 2, -2, 0, 1], 'euler11': [1, 1, 0], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, 2, 19], 'euler2': [1, 1, 0], 'euler23': [1, 3, 23], 'euler29': [1, 1, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, -2, 37], 'euler41': [1, -5, 41], 'euler43': [1, -11, 43], 'euler47': [1, -11, 47], 'euler5': [1, 1, 0], 'euler53': [1, 11, 53], 'euler59': [1, 6, 59], 'euler61': [1, 14, 61], 'euler67': [1, 14, 67], 'euler7': [1, 3, 7], 'euler71': [1, -6, 71], 'euler73': [1, 11, 73], 'euler79': [1, 8, 79], 'euler83': [1, -8, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 3, 7], [1, 1, 0], [1, 0, 0], [1, 2, 17], [1, 2, 19], [1, 3, 23], [1, 1, 29], [1, 7, 31], [1, -2, 37], [1, -5, 41], [1, -11, 43], [1, -11, 47], [1, 11, 53], [1, 6, 59], [1, 14, 61], [1, 14, 67], [1, -6, 71], [1, 11, 73], [1, 8, 79], [1, -8, 83], [1, 6, 89], [1, -2, 97]], 'index': 133, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/167310/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-167310-1.1-c1-0-133', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-167310-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.551020180263684, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 374231784193537715, 'z1': {'__RealLiteral__': 0, 'data': '1.055428487996775', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '374231784193537715', 'Lhash_array': ['374231784193537715'], 'factors': ['2-167310-1.1-c1-0-133'], 'label': '2-167310-1.1-c1-0-133', 'type': 'ECQ', 'url': 'EllipticCurve/Q/167310/e'}